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%I #26 Sep 08 2022 08:45:15
%S 1,9,34,86,175,311,504,764,1101,1525,2046,2674,3419,4291,5300,6456,
%T 7769,9249,10906,12750,14791,17039,19504,22196,25125,28301,31734,
%U 35434,39411,43675,48236,53104
%N Structured heptagonal diamond numbers (vertex structure 5).
%H Vincenzo Librandi, <a href="/A100179/b100179.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = (1/6)*(10*n^3 - 9*n^2 + 5*n).
%F G.f.: x*(1 + 5*x + 4*x^2)/(1-x)^4. - _Colin Barker_, Jan 19 2012
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - _Harvey P. Dale_, Oct 28 2018
%F E.g.f.: (6*x + 21*x^2 + 10*x^3)*exp(x)/6. - _G. C. Greubel_, Nov 08 2018
%t Table[(10n^3-9n^2+5n)/6,{n,40}] (* _Harvey P. Dale_, Oct 28 2018 *)
%o (Magma) [(1/6)*(10*n^3-9*n^2+5*n): n in [1..40]]; // _Vincenzo Librandi_, Aug 18 2011
%o (PARI) vector(40, n, (10*n^3-9*n^2+5*n)/6) \\ _G. C. Greubel_, Nov 08 2018
%Y Cf. A004126 = alternate vertex; A000447 = structured diamonds; A100145 for more on structured numbers.
%K nonn,easy
%O 1,2
%A James A. Record (james.record(AT)gmail.com), Nov 07 2004
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